SSAT Upper Level Quantitative - How to find the reciprocal of a fraction

Give the reciprocal of 0.8.

Explanation

The reciprocal of a number is the quotient of 1 and that number. Divide 1 by 0.8 by moving the decimal point to the right in each number one place:

$1 \div 0.8 = 10 \div 8 = 1.25$

Add the reciprocals of 0.3 and 0.7. What is their sum?

$4\frac{16}{21}$

$\frac{21}{100}$

$2\frac{8}{21}$

The correct answer is not among the other responses.

Explanation

$0.3 = \frac{3}{10}$ , so its reciprocal is $\frac{10}{3}$ .

$0.7= \frac{7}{10}$ , so its reciprocal is $\frac{10}{7}$ .

Add them:

$\frac{10}{3} + \frac{10}{7} = \frac{10 \cdot 7 }{3 \cdot 7} + \frac{10\cdot 3}{7\cdot 3} = \frac{70}{21}+\frac{30}{21} = \frac{100}{21}$

$100 \div 21 = 4 \textup{ R }16$ , so

$\frac{100}{21}= 4\frac{16}{21}$

Let be the reciprocal of 0.22. Which of the following is true of ?

Explanation

$0.22 = \frac{22}{100}$ , so its reciprocal is $N= \frac{100}{22}$ .

Since $100 \div 22 = 4\textup{ R }12$ ,

$N= \frac{100}{22} = 4 \frac{12}{22}=4\frac{6}{11}$

Therefore, .

Let be the reciprocal of 1.77. Which of the following is true of ?

Explanation

$1.77= \frac{177}{100}$ , so its reciprocal is $N= \frac{100}{177}$ .

If 100 is divided by 177, the decimal equivalent is seen to be so

Subtract the reciprocal of 1.5 from the reciprocal of 0.125. What is the result?

$7\frac{1}{3}$

$\frac{13}{24}$

$\frac{8}{11}$

$6\frac{1}{2}$

The correct answer is not among the other responses.

Explanation

$1.5 = \frac{15}{10} = \frac{3}{2}$ , so its reciprocal is $\frac{2}{3}$ .

$0.125 = \frac{125}{1,000} = \frac{1}{8}$ , so its reciprocal is 8.

The requested difference is $8-\frac{2}{3} = 7\frac{1}{3}$

Give the reciprocal of 0.75.

$1 \frac{1}{3}$

$-1 \frac{1}{3}$

Explanation

The reciprocal of a number is the quotient of 1 and the number.

Divide 1 by 0.75 by moving the decimal point to the right in each number two places:

$1 \div 0.75 = 100 \div 75 = 1 \frac{25}{75} = 1 \frac{1}{3}$

Subtract the reciprocal of 11 from the reciprocal of 13. What is the result?

$\text{The correct answer is not among the other responses.}$

$\frac{2}{143}$

$\frac{1}{2}$

$\frac{24}{143}$

$\frac{1}{24}$

Explanation

The reciprocals of 11 and 13 are, respectively, $\frac{1}{11}$ and $\frac{1}{13}$ . The requested difference is

$\frac{1}{13}-\frac{1}{11} = \frac{1\cdot 11}{13 \cdot 11}-\frac{1\cdot 13}{11 \cdot 13} = \frac{1 1}{143 }-\frac{ 13}{143} =-\frac{2}{143}$

This answer is not among the given choices.

Add the reciprocals of , , and . What is the sum?

$\frac{13}{24}$

$\frac{11}{24}$

$\frac{1}{6}$

$\frac{1}{18}$

$\frac{15}{24}$

Explanation

The reciprocals of 4, 6, and 8 are, respectively, $\frac{1}{4}, \frac{1}{6}, \frac{1}{8}$ . Their sum is

$\frac{1}{4}+\frac{1}{6}+ \frac{1}{8}$

First we find the least common denominator between all three fractions.

$= \frac{1}{4}\bigg(\frac{6}{6}\bigg) + \frac{1}{6}\bigg(\frac{4}{4}\bigg) +\frac{1}{8}\bigg(\frac{3}{3}\bigg)$

$=\frac{6}{24}+\frac{4}{24}+\frac{3}{24} = \frac{13}{24}$

How to find the reciprocal of a fraction

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